Black holes are perhaps the most perfectly thermal objects in the universe. Explaining the microscopic origin of their thermal nature is a long-standing problem in theoretical physics.
In the mid-seventies Bekenstein and Hawking discovered that black holes have an entropy. A black hole can be perturbed away from its equilibrium state, for instance by letting some matter fall into it. When the system reaches equilibrium again, the area A of the black hole horizon has grown by an amount δA. The increase in the entropy δS of the black hole is given by the Bekenstein-Hawking formula,
where κ is Boltzmann's constant, c the speed of light, G Newton's constant, and ℏ Planck's constant. Since Bekenstein and Hawking's discovery, various physical mechanisms have been proposed to explain the microscopic origin of such entropy. The appearance of Planck's constant ℏ in the entropy indicates that the phenomenon has a quantum nature. The presence of Newton's constant together with ℏ suggests that a theory of quantum gravity is needed to explain the phenomenon. What is the quantum nature of this entropy?
Both String Theory and Loop Quantum Gravity have claimed a partial success in deriving the Bekenstein-Hawking entropy. The proposed explanations seem to follow the standard argument appropriate for an ordinary thermodynamic system, like a gas in a box: the Boltzmann entropy of the system is the logarithm of the number of accessible states. But is it really the case that we have to count states to explain the origin of black hole entropy?
Here I argue that the horizon of a black hole is not like a gas in a box: its entropy is not due to a large number of states, but to just one single state! The Bekenstein-Hawking area law for the entropy of a black hole is due to quantum correlations of gravity and matter across the horizon of the black hole, i.e. to entanglement.
Quantum entanglement has long been suspected to be the physical mechanism behind the entropy of black holes. After all, in the presence of a horizon, we know that all quantum fields are in a thermal state exactly because of entanglement. The horizon is hot because of entanglement, and it is reasonable to expect that the two thermal properties - the entropy and the temperature of the horizon - are explained by the same physical phenomenon. However, the actual mechanism that explains why the Bekenstein-Hawking formula is universal has remained obscure until recently. If there are two scalar fields instead than one, shouldn't the entropy be twice as large?
The resolution of the puzzle comes from realizing that in thermodynamics the physically relevant quantity is not the entropy in itself, but how the entropy changes in a physical process. Low-energy perturbations of the entanglement entropy are universal and reproduce the area law. This universality is explained by the same mechanism behind the "accident" that the inertial mass equals the gravitational charge, a quantum version of Einstein's equivalence principle.
From arXiv:1211.0522, E.Bianchi 2012.